STUDIES ON FLUIDIZATION CHARACTERSTICS OF...

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STUDIES ON FLUIDIZATION CHARACTERSTICS

OF FINE PARTICLES IN A GAS-SOLID FLUIDIZED

BED

A Project submitted to the

National Institute of Technology, Rourkela

In partial fulfillment of the requirements

of

Bachelor of Technology (Chemical Engineering)

By

Debashis Biswal

Roll No. 10600027

Under the guidance of

Prof. Abanti Sahoo

DEPARTMENT OF CHEMICAL ENGINEERING

NATIONAL INSTITUTE OF TECHNOLOGY, ROURKELA

ORISSA -769 008, INDIA

2010

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DEPARTMENT OF CHEMICAL

ENGINEERING

NATIONAL INSTITUTE OF TECHNOLOGY,

ROURKELA -769 008, INDIA

CERTIFICATE

This is to certify that the thesis entitled STUDIES ON FLUIDIZATION

CHARACTERSTICS OF FINE PARTICLES IN A GAS-SOLID FLUIDIZED BED ,

submitted by Debashis Biswal to National Institute of Technology, Rourkela is a record of

bonafide project work under my supervision and is worthy for the partial fulfillment of the

degree of Bachelor of Technology (Chemical Engineering) of the Institute. The candidate has

fulfilled all prescribed requirements and the thesis, which is based on candidate’s own work, has

not been submitted elsewhere.

Supervisor

Prof. Abanti Sahoo

Department of Chemical Engineering

National Institute of Technology

Rourkela - 769008

INDIA

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ACKNOWLEDGEMENT

It is with a feeling of great pleasure that I express my most sincere heartfelt gratitude to

Prof. (Dr.) Abanti Sahoo for suggesting the topic for my project and for her ready and able

guidance through out the course of preparing report. I am greatly indebted to her for constructive

suggestions and criticisms from time to time during the progress of my work.

I thank the staff members of my department for their invaluable help and guidance. Lastly;

I thank all my class mates, who have helped me in the completion of my report.

DEBASHIS BISWAL

Roll NO: -10600027

B.Tech. (8th Semester)

iv

Abstract

Attempt has been made to study the fluidization characteristics of fine particles in a gas-solid

system. Experiments on the fluidization of fine-particles of different sizes and densities were

carried were carried out in a cylindrical column of 5cm dia. Fluidization characteristics such as

bed expansion, bed fluctuation, bed pressure drop in turn the Euler Number of fine particles have

been tried to be analysed by varying the different system parameters. In the present work,

attempt has been made to fluidize fine particles by changing the surface property of the particles

using a stirrer. These fluidization characteristics have been correlated against the different

system parameters (viz. static bed height, particle size, particle density, speed of the stirrer and

superficial velocity of the medium) on the basis of Dimensionless Analysis approach. Finally

calculated values of different fluidization characteristics have been compared against the

experimentally observed values. The result show a good agreement among the experimental and

calculated values thereby indicating the application of these developed correlations over a wide

range of parameters.

Key-Words: Bed expansion and Bed-Fluctuation Ratio, Euler’s No., Fluidized bed

with the stirrer

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CONTENTS

CHAPTER Title Page No.

No.

1. Introduction 02

2. Literature Review 04

2.1 Bubbling 04

2.2 Slugging 04

2.3 Channeling 05

2.4 Minimum Fluidization Velocity 05

2.5 Pressure Drop 06

2.6 Bed Expansion Ratio (R) 07

2.7 Bed Fluctuation Ratio (r) 07

2.8 Euler Number 07

3. Experimental Set-up 08

3.1 Experimental Work 09

4. Results And Discussion 10

4.1 Observations 10

4.2 Development Of Correlation 16

4.3 Final Results 32

4.4 Discussion 33

5. Conclusion 34

Appendix Experimental Data 36-62

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LIST OF TABLES

Table No Title Page No

1 Scope of the Experiment 19

2 Observed Data & Comparison of 20

Calculated Value of Expansion Ratio ‘R’

With Experimental ‘R’ Value

3 Observed Data and Comparison of 25

Calculated Value of Fluctuation Ratio ‘r’

With Experimental ‘r’ Value

4 Observed Data & Comparison of 30

Calculated Value of Euler Number ‘EN’

With Experimental ‘EN’ Value

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LIST OF FIGURES

Figure No Title Page No

3.1 Schematic View of the Experimental Set-up 8

3.2 Laboratory Set-up 9

4.1.1-4.1.6 Variation of ∆∆∆∆p with superficial velocity 10-15

(Uo)

4.2.1-4.2.5 ‘ R ‘ Vs Different Parameters 16-18

4.2.6 CORRELATION PLOT OF BED EXPANSION 21

RATIO AGAINST SYSTEM PARAMETERS

4.2.7-4.2.11 ‘ r ‘ Vs Different Parameters 22-24

4.2.12 CORRELATION PLOT OF BED FLUCTUATION 26

RATIO AGAINST SYSTEM PARAMETERS

4.2.13-4.2.17 ‘ E.N ‘ Vs Different Parameters 27-29

4.2.18 CORRELATION PLOT OF EULER NUMBER 31

AGAINST SYSTEM PARAMETERS

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NOMENCLATURE

dp: Particle diameter

Dc: Column diameter

∆P : Pressure difference

UO: Superficial velocity

Umf: Minimum fluidization velocity

Uavg: (Uo-Umf)

Hs: Static bed height

N: Speed of stirrer

ρs : Density of solid

ρf : Density of fluid

€mf = Voidage ;

µ f = Viscosity of fluid;

Фs= Sphericity ;

SUBSCRIPTS

avg- average

del- Delta

E.N- Euler’s No

mf- minimum fluidization

sup- superficial

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CHAPTER 1

2

INTRODUCTION

Gas-solid fluidiziations have found more industrial applications due to good solid-fluid

mixing. The important advantages of the gas-solid fluidized beds are smooth, liquid-like flow of

solid particles. This permits a continuous automatically-controlled operation with ease of

handling and rapid mixing of solids which leads to a near isothermal condition throughout the

bed. This results in a simple and controlled operation with rapid heat and mass transfer rates

between gas and particles, thereby minimizing overheating in case of heat sensitive products.

Some of the important applications of gas-solid fluidized beds are in the dairy, cement

industries, food and pharmaceutical industries for drying, cooling, coating and agglomeration.

Formation of large scale bubbles during the fluidization reduces the heat and mass

transfer rate which affect the output of the system. Hence persistent effort have been made by

the investigators to improve the quality of gas-solid fluidization by promoting bubble breakage

and hindering the coalescence of bubbles which result in reduced bed expansion and fluctuation

and better gas-solid mixing .This is the main disadvantage when the fluidized bed are used in

chemical and petrochemical industry where it fluidization is accompanying with chemical

reaction. Reducing in gas-solid mixing reduces the rate of chemical reaction.

Fluidization quality is closely related to particle intrinsic properties such as particle

size, particle density ,size distribution of particle and its surface characteristics. As the particle

size decreases the cohesive force ( i.e. Vander Wall Force) for the particle increases. So due to

this effect the method of fluidization for fine particle becomes much more difficult as compared

to the larger size particle. It was also pointed out by Geldart in his classification map, fine

particle in Group C (small particle size and low particle density) fluidize poorly due to their

strong inter-particle cohesive forces, exhibiting channeling, lifting as a plug and forming ‘‘rat

holes’’ when aerated. Therefore, the development of reliable techniques to improve the

fluidization of cohesive fine powders is required. Several external devices based on using

vibration and mechanical agitation have been suggested to improve the flow ability of

cohesive fine particle. Despite the use of these devices, handling of fine particle is still

extremely difficult and wet processing, such as coating and granulation of fine particle has been

regarded as nearly impossible.

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Preconditioning methods have been developed that help to decrease cohesion, which

results in non-bubbling fluid-like fluidization of fine powders. For example, xerographic

toners (powders of micron sized particles), with cohesion reduced by surface coating, have been

shown to transit from the solid-like regime to uniform non-bubbling fluidization as the gas flow

is increased. Experimental results have shown that it was possible to improve fluidization

uniformity of Ni/SiO2 aerogels by decreasing the strength of inter-particle forces, which could

be influenced by initial bed compaction, gas moisture content and admixture of inert particles

and the oxidized state of Ni .

The type of fluidizing gas also significantly affects the fluidization quality of fine

particles. It has been found that the fluidization behaviour of Geldart group A particles is

strongly dependent on the type of fluidizing gas. In the work of Geldart and Abrahamsen

(1978), it has been demonstrated that the bubbling and bed expansion behaviours of group A

particles of alumina and glass beads greatly differ with the type and pressure of the fluidizing

gas. It has been observed that a group A powder may behave more "A-like" when using

different types of fluidizing gas. According to Piepers et al. (1984), physically adsorbed gases

may enhance the cohesion of particles, resulting in an increased elastic modulus of a fluidized

bed and a growth in the bed expansion.

In the present experimental work fluidization of fine particle had been carried out in a 2-

dimensional fluidized bed with the help of a stirrer. With the application of stirrer in the

fluidized bed ,the general problem of fluidizing fine particle such as channeling, slugging etc.

had been counter reacted. Different size fine particle of different material are used for the

experiments. There variation with various parameter such as particle size (dp), bed height (Hs),

superficial velocity (Uo) and rotational speed of stirrer (N) had been studied. The correlations

for (1) expansion ratio ‘R’,(2) fluctuation ratio ‘r’ and (3) Euler number with the above

mentioned parameter have been developed.

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CHAPTER 2

LITERATURE REVIEW

Fluidization is an established fluid-solid contacting technique. A fluidized bed can be

achieved by increasing the upward velocity of the fluid through a fixed bed of solid particles.

Fluidized bed technique as compared to fixed bed has the unique advantage of a smooth,

liquidlike flow of solid particles which allows continuous and automatically-controlled

operation with ease of handling and rapid mixing of solids. In spite of these advantage, the

applications of gas-solid fluidized bed have been constrained due to certain inherent drawbacks

like channelling, uncontrolled bed expansion and fluctuation because of formation of bubbles

and their subsequent collapsing, and slugging. These not only reduce the heat and mass transfer

rate thereby affecting the outcome of the system, but influence the fluidization quality to a

considerable extent. When the particle size reduces these problems predominant in the

fluidization process . A brief survey on these problem had been made in the following :-

2.1 Bubbling: A gas-solid fluidized bed is characterized by the presence of gas voids or

bubbles causing a resistance to mass and heat transfer. Bubbles in gas fluidized bed are very

important as they are responsible for most of the features that differentiate a packed bed from a

fluidized one. The quality of fluidization specially in terms of expansion and fluctuation

depends largely on the formation of bubbles and their growth in the direction of flow.

Modification of gas flow promotes the formation of bubbles of smaller size through the system

and cause particle movement which generally results reduced expansion and fluctuation, rapid

and extensive particle mixing and a consequent high heat transfer co-efficient.

2.2 Slugging: The gas-solid fluidization is characterized by the formation of bubble. The size

of the bubble increases and sometimes even its diameter may become equal to that of the

column. When the bubble diameter approaches the column diameter, it is termed as slugging.

An aggregatively fluidized bed in a column of small diameter operated at sufficiently high gas

velocity will show continuous slug flow. Slugging affects adversely the fluidization quality.

Once slugging occurs, the portion of the bed above the bubble is pushed upwards, as by a

piston. Particle rain down from the slug and the slug finally disintegrates. Periodically another

slug forms and thus unstable oscillatory motion is repeated. Slugging increases the problem of

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entrainment and lowers the performance potential of the bed. Slugging is especially serious in

long narrow fluidized beds.

2.3 Channeling: The quality of fluidization specially in term of mixing is greatly affected

by channeling. As the flow rate through a bed of particle increases towards minimum

fluidization of the bed materials, channeling may occur. The non-uniformity in size of bed

materials and poor mixing between the fluid and the particles in the bed may lead to channeling.

At the onset of the formation of channeling, the fluid tends to pass through the bed along such

paths of lower particle concentration. Channeling can result from initial non-uniformity in the

bed and tends to be accentuated by stickiness of the particle which prevents them from flowing

into the channeled region. Where the fluid velocity is significant, the solid particles develop an

upward movement, while in case of lower fluid velocity they go downwards. The local increase

in velocity through the bed above minimum fluidization, causes the bed to locally expand,

thereby altering the pressure drop through that portion of the bed. The change in local pressure

drop through the distributor and the combined pressure drop of the bed and the distributor

quantify the channeling. A channel tends to become established if the local pressure drop

through the bed-distributor system decreases with increased fluid velocity.

Apart from these the parameter that are studied during a fluidization process are:

• Minimum Fluidization Velocity (Umf)

• Pressure Drop (∆p)

• Bed Expansion Ratio (R)

• Bed Fluctuation Ratio (r)

2.4 Minimum Fluidization Velocity: When a fluid passes upwards through the

interstices of a bed of solids without the slightest disturbance of the solids, the bed is called a

fixed bed. With further increase in the velocity of fluid, the entire bed of solids is suspended and

behaves as if its weight is counterbalanced by the force of buoyancy. At this point, the bed of

solids starts behaving like a fluid. This is called onset of fluidization and the velocity of fluid at

which it happens is called minimum fluidization velocity, which is one of the most important

parameter for the design of fluidizers.

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There are several correlations on minimum fluidization velocity proposed by Leva [57] , Rowe

and Henwood[58], Narsimhan [59], Wen and Yu [60], Richardson [61] etc.. Out of which

Ergun’s correlation [62] being used over a wide range of Reynolds number is given below:

(1)

Where :

∆pb = Pressure drop across bed ;

hs = Static bed height ;

€mf = Voidage ;

µ f = Viscosity of fluid;

Umf= Minimum fluidization velocity;

ρf = Density of fluid;

Фs= Sphericity ;

2.5 Pressure Drop: The pressure drop through the bed is another important parameter

which controls the channel and slug formation and thereby mixing of the bed material with the

fluidizing fluid. At low flow rates in the packed bed, the pressure drop is approximately

proportional to gas velocity upto the minimum fluidization condition. With a further increase in

gas velocity, the packed bed suddenly unlocks (at the onset of minimum fluidization condition),

resulting in a decrease in pressure drop. With gas velocities beyond minimum fluidization, the

bed expands and gas bubbles are seen to rise resulting in nonhomogeneity in the bed. With the

increase in gas flow, the pressure drop should remain unchanged but due to bubbling and

slugging there is always a fluctuation in the pressure drop and it increases slightly . Particularly

for coarse particles, the mean total pressure drop across a slugging bed may continue to increase

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with gas velocity higher than at the minimum fluidization condition. For fine particles the

variation of pressure drop with gas velocity is quasi-linear when they are fluidized by classical

method of fluidization as they form cranks and channel. Particulate fluidization generally gives

rise to a homogeneous fluidization. However, this ideal situation is not realized in practice and

significant deviations have been observed.

2.6 Bed Expansion Ratio (R) : Expansion of gas-solid fluidized beds may in general

result from the volume occupied by bubbles and from increase in voidage of the dense phase.

Bed Expansion Ratio (R) is defined as the ratio of average height of bed (Havg) i.e

(Hmax+Hmin)/2 and Static bed height Hs. Bed expansion ratio increases with increasing value

of excess velocity and for distributors which give smaller bubbles. Very poor distributors which

lead to channeling condition rather than bubbling reduce bed expansion ratio. Many Empirical

relation for ‘R’ had been developed earlier using different experimental data.

2.7 Bed Fluctuation Ratio (r) : For gas flow more than the minimum fluidization

velocity, the top of the fluidized bed may fluctuate considerably. The extent of the fluctuation

and its estimation becomes important while specifying the height of a fluidizer. The fluctuation

ratio ‘r’ is the ratio of the highest and the lowest level of the top of the bed for any fluidizing

gas velocity. Consistent effort had been made to correlate fluctuation ratio in terms of static and

dynamic parameters of the system as the bed fluctuation and fluidization quality are being inter

related.

2.8 Euler Number (∆∆∆∆p/Uo2ρf) : The Euler Number is a dimensionless value commonly

used for analyzing fluid flow dynamics problems where the pressure difference between two

point is an important variable. The Euler Number can be interpreted as a measure of the ratio of

pressure forces to inertial forces. Euler number is useful in analyising the pressure variation

with other parameter of fluidization.

8

CHAPTER 3

EXPERIMENTAL SETUP

The experimental set-up consists of a fluidizer, rotameter, manometer, compressor, varriac-

motor as shown in Fig-3.1 . The fluidization is carried out in side a cylindrical tube of dia.

‘5cm’.The distributor used for the process is packed bed type above which a filter cloth is placed.

From the top of the bed a stirrer with a rod promoter is placed inside the tube to provide constant

rotation. The rotameter used in the setup is of 0-10 lpm capacity. The tube is closed with filter

cloth at the top to stop the entrainment of the particles. Two tubes one at top & another at

bottom is connected to the manometer to measure the ∆P. Liquid used in the manometer is CCl4.

The distributor is packed with glass beads of uniform size so as to get uniform distribution of

fluid to avoid channeling.

Figure 3.1 : Schematic View of the Experimental Set-up

Apparatus in the set-up:

1:Compressor;2:receiver;3:Silicageltower, 4:By pass valve; 5:Line valve; 6:rotameter;7:Packed

bed distributor; 8:fluidize bed;9:Stirrer with rod-promotor; 10:mano meter; 12:Variac;

9

Figure 3.2 :Laboratory Set-up

3.1 Experimental Work :

� The fluidization is carried out with

talcum powder (particle size dp=65µm

& dp=80µm),alumina powder (particle

size dp=75µm),silicon carbide (particle

size dp=70µm) and magnetite ore

(particle size dp=60µm).

� With one fixed bed height the by varying

the RPM of the stirrer four different

experiment were done.

� Again with fixed rpm with different bed

height experiment were carried out.

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CHAPTER 4

RESULTS AND DISCUSSION

4.1 OBSERVATION (Variation of ∆∆∆∆p with superficial velocity (Uo))

4.1. 1 Material-Talcum Powder (dp=65 µm)

Figure 4.1.1 : With varying rpms of stirrer

1

10

100

1000

10000

0.001 0.01 0.1 1

∆∆∆∆ P

(N/m2)

Usup.

del P

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Usup

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Usup0.1

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Usup

Hs=16 cm,73.9 rpm Hs=16 cm,101.6 rpm

Hs=16 cm,121.2 rpm Hs=16 cm,137.4 rpm

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Figure 4.1.2 : With varying Static bed heights, Hs

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo

121.2 rpm,,Hs=16cm

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo

121.2 rpm,,Hs=22cm

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo121.2 rpm,,Hs=25cm

1E-13

1E-11

1E-09

0.000000

0.00001

0.001

0.1

10

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo121.2 rpm,,Hs=28cm

4.1.2 Material-Talcum Powder(dp=80

Figure 4.1.3 : With varying

0.001 0.01 0.1

∆ P

(N/m2)

Uo

(At 73.9 rpm)

Hs=16cm

0.001 0.01 0.1

∆ P

(N/m2)

Uo

At 121.2 rpm

Hs=16cm

0.001 0.01 0.1

∆ P

(N/m2)

(At 121.2rpm)

(Hs=18cm)

Uo

12

Talcum Powder(dp=80 µm)

Figure 4.1.3 : With varying rpms of stirrer & Static bed heights, Hs

1

10

100

1000

10000

1

73.9 rpm)

0.001 0.01

∆ P

(N/m2)

1

10

100

1000

10000

0.1 1

At 121.2 rpm

0.001 0.01

∆ P

(N/m2)

1

10

100

1000

10000

1

121.2rpm)

0.001 0.01

∆ P

(N/m2)

1

10

100

1000

10000

0.01 0.1 1Uo

(At 101.6 rpm)

Hs=16cm

1

10

100

1000

10000

0.01 0.1 1Uo

(At 137.4rpm)

1

10

100

1000

10000

0.01 0.1 1Uo

(At 121.3rpm)

(Hs-21cm)

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4.1.3 Material- Alumina Powder(dp=75 µm)

Figure 4.1.4 : With varying rpms of stirrer & Static bed heights, Hs

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo

73.9rpm

1E-13

1E-10

0.000000

0.0001

0.1

100

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo

101.6 rpm

Hs=16cm

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo

121.2 rpm

Hs=16cm

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo

137.4 rpm

Hs=16cm

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo (m/sec)

Hs=18cm,121.2 rpm

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo

Hs=21cm,121.2 rpm

Hs=16cm

14

4.1.4 Material- Silicon Carbide(dp=70 µm)


1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo

73.9 rpm

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

U0

101.6rpm

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo

121.2rpm

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo

137.4rpm

15

4.1.5 Material- Magnetite(dp=60 µm)


1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo

73.9 rpm

Hs=16cm

1

10

100

1000

10000

0.001 0.01 0.1 1

∆ P

(N/m2)

Uo

101.6 rpm

1

10

100

1000

10000

0.001 0.01 0.1 1

∆p (N/m2)

Uo

121.2 rpm

1

10

100

1000

10000

0.001 0.01 0.1 1

∆p (N/m2)

Uo

137.4 rpm

4.2 DEVELOPMENT OF

4.2.1 FOR BED EXPANSION RATIO (R)

Exponents Of Individual Parameter

(Uo-

Umf)/Umf

R

0.697793 2.625

1.037351 2.765

1.37691 2.8125

1.716469 2.875

Hs/Dc R

3.2 2.75

4.4 2.25

5 2.06

5.6 1.294643

1

10

R

1

10

1

R

R Vs (Uo-Umf)/Umf

R Vs Hs/Dc

16

DEVELOPMENT OF CORRELATION

FOR BED EXPANSION RATIO (R)

Of Individual Parameters :

Figure 4.2.2 : R Vs Hs/Dc

y = 2.731x0.098

1

10

0.1 1(Uo-Umf)/Uo

y = 11.36x-1.15

1

R

Hs/Dc

R=11.36 ( Hs/Dc)-1.15

R=2.731((Uo-Umf)/Umf))0.098

Figure- 4.2.1: R Vs (Uo-Umf)/Umf

10

10

N R

73.9 2.8125

101.6 2.75

121.2 2.75

137.4 2.71875

ρs/ρf R

708.6614 2.75

2968.504 1.625

2519.685 1.625

4094.488 1.78125

1

10

10

R

1

10

R

R Vs N

R Vs ρs/ρf

17

Figure 4.2.3: R Vs N

Figure 4.2.4: R Vs ρs/ρf

y = 3.495x-0.05

100N (rpm)

R= 3.495 N-0.05

y = 18.52x-0.29

100 1000

R

ρs/ρf

R=18.52 (ρs/ρf)-0.29

1000

10000

18

dp/Dc R

0.0013 2.75

0.0014 2.47149

0.0015 1.8601

0.0016 1.5625

Figure 4.2.5 : R Vs dp/Dc

y = 2E-08x-2.85

1

10

0.001 0.01

R

dp/DcR Vs dp/Dc

R = 2E-08(dp/Dc)-2.85

19

Table 1 : Scope of the Experiment

S.l.No Materials Uo/Umf Hs, cm N, rpm ρs, g/cc dp in µm

1 Talcum Powder 1.25 16 73.9 0.9 65

2 Talcum Powder 1.5 16 73.9 0.9 65

3 Talcum Powder 1.75 16 73.9 0.9 65

4 Talcum Powder 2.0 16 73.9 0.9 65

5 Talcum Powder 1.75 16 121.2 0.9 65

6 Talcum Powder 1.75 22 121.2 0.9 65

7 Talcum Powder 1.75 25 121.2 0.9 65

8 Talcum Powder 1.75 28 121.2 0.9 65

9 Talcum Powder 1.75 16 73.9 0.9 65

10 Talcum Powder 1.75 16 101.6 0.9 65

11 Talcum Powder 1.75 16 121.2 0.9 65

12 Talcum Powder 1.75 16 137.4 0.9 65

13 Talcum Powder 1.75 16 121.2 0.9 65

14 Alumina 1.75 16 121.2 3.77 75

15 SiC 1.75 16 121.2 3.2 70

16 Magnetite 1.75 16 121.2 5.2 60

17 Talcum Powder 1.75 16 121.2 0.9 65

18 Talcum Powder 1.75 16 121.2 0.9 70

19 Talcum Powder 1.75 16 121.2 0.9 75

20 Talcum Powder 1.75 16 121.2 0.9 80

20

Table 2 –Observed Data & Comparison of Calculated Value of Expansion Ratio ‘R’

With Experimental ‘R’ Value

Del

U/Umf

Hs/Dc N, rpm ρs/ρf dp/Dc product R-exp R-Cal %dev

0.698 3.200 73.900 708.661 0.001 5116402.470 2.625 2.758 -5.05

1.037 3.200 73.900 708.661 0.001 5319125.534 2.766 2.849 -3.03

1.377 3.200 73.900 708.661 0.001 5468802.570 2.813 2.917 -3.71

1.716 3.200 73.900 708.661 0.001 5588224.109 2.875 2.971 -3.33

1.377 3.200 73.900 708.661 0.001 5468802.570 2.750 2.917 -6.07

1.377 4.400 73.900 708.661 0.001 3791788.824 2.250 2.141 4.83

1.377 5.000 73.900 708.661 0.001 3273401.033 2.060 1.892 8.18

1.377 3.200 73.900 708.661 0.001 5468802.570 2.813 2.917 -3.71

1.377 3.200 101.600 708.661 0.001 5382447.242 2.750 2.878 -4.66

1.377 3.200 121.200 708.661 0.001 5335183.190 2.750 2.857 -3.88

1.377 3.200 137.400 708.661 0.001 5301821.847 2.719 2.842 -4.52

1.377 3.200 121.200 708.661 0.001 5335183.190 2.750 2.857 -3.88

1.377 3.200 121.200 2968.504 0.002 2342173.905 1.625 1.426 12.25

1.377 3.200 121.200 2519.685 0.001 2989921.750 1.625 1.752 -7.83

1.377 3.200 121.200 708.661 0.001 5335183.190 2.750 2.857 -3.88

1.377 3.200 121.200 708.661 0.001 4319395.668 2.471 2.390 3.29

1.377 3.200 121.200 708.661 0.002 3548361.037 1.860 2.025 -8.85

1.377 3.200 121.200 708.661 0.002 2952201.112 1.563 1.734 -10.95

21

Figure 4.2.6 : CORRELATION PLOT OF BED EXPANSION RATIO AGAINST

SYSTEM PARAMETERS

y = 6E-06x0.844

R² = 0.871

1

10

1000000 10000000

R

e

x

p

t

PRODUCT

( )4064.2246.0

042.0

971.0083.0

066

−−

−

−

−×−=

c

p

f

s

c

s

mf

mfo

D

dN

D

H

U

UUER

ρ

ρ

4.2.2 FOR BED FLUCTUATION RATIO (r)

Exponent Of Individual Parameter :

Uavg/Umf r

1.037351 1.1

1.37691 1.097561

1.716469 1.146341

2.056027 1.180723

Figure

Hs/Dc r

0.32 1.146341

0.44 1.181818

0.5 1.2

0.56 1.230769

1

10

1

r

1

10

0.1

r

r Vs (Uavg/Umf)

r Vs Hs/Dc

22

FOR BED FLUCTUATION RATIO (r)


Figure-4.2.7 : r Vs (Uavg/Umf)

Figure 4.2.8: r Vs Hs/Dc

y = 1.082x0.108

1

r

Uavg/Umf

y = 1.311x0.120

Hs/Dc

r = 1.082(Uavg/Umf )

0.108

r= 1.311 (Hs/Dc )

0.120

10

1

N r

73.9 1.195122

101.6 1.097561

129.2 1.146341

137.4 1.175

ρs/ρf r

708.6614 1.146341

2968.504 1.363636

2519.685 1.363636

4094.488 1.375

y = 1.339x

1

10

10

r

y = 0.554x

1

10

100

r

r Vs N

r Vs (ρs/ρf)

23

Figure 4.2.9 : r Vs N

Figure 4.2.10 : r Vs (ρs/ρf)

y = 1.339x-0.03

100N

y = 0.554x0.111

1000ρs/ρf

r = 1.339N-0.03

r = 0.554 (ρs/ρf)0.111

1000

10000

24

dp/Dc r

0.0013 1.146341

0.0014 1.24241

0.0015 1.542975

0.0016 1.631579

Figure 4.2.11: r Vs (dp/Dc)

y = 23715x1.843

1

10

0.001 0.01

r

dp/Dc

r = 23715(dp/Dc)1.843

r Vs (dp/Dc)

25

Table 3 Observed Data and Comparison of Calculated Value of Fluctuation Ratio ‘r’

With Experimental ‘r’ Value

Uavg/Umf Hs/Dc N, rpm ρs/ρf dp/Dc product r exp r cal %dev

1.037 0.320 101.600 708.661 0.001 0.0000075 1.100 1.135 -3.19

1.377 0.320 101.600 708.661 0.001 0.0000077 1.098 1.160 -5.66

1.716 0.320 101.600 708.661 0.001 0.0000079 1.146 1.179 -2.87

2.056 0.320 101.600 708.661 0.001 0.0000080 1.181 1.195 -1.24

1.377 0.320 129.200 708.661 0.001 0.0000077 1.146 1.154 -0.65

1.377 0.440 129.200 708.661 0.001 0.0000080 1.182 1.187 -0.42

1.377 0.500 129.200 708.661 0.001 0.0000081 1.200 1.200 -0.02

1.377 0.560 129.200 708.661 0.001 0.0000082 1.231 1.212 1.50

1.377 0.320 73.900 708.661 0.001 0.0000078 1.195 1.167 2.31

1.377 0.320 101.600 708.661 0.001 0.0000077 1.098 1.160 -5.66

1.377 0.320 129.200 708.661 0.001 0.0000077 1.146 1.154 -0.65

1.377 0.320 137.400 708.661 0.001 0.0000076 1.175 1.152 1.93

1.377 0.320 129.200 708.661 0.001 0.0000077 1.146 1.154 -0.65

1.377 0.320 129.200 2968.504 0.002 0.0000117 1.364 1.550 -13.68

1.377 0.320 129.200 2519.685 0.001 0.0000101 1.364 1.400 -2.68

1.377 0.320 129.200 4094.488 0.001 0.0000080 1.375 1.191 13.37

1.377 0.320 129.200 708.661 0.001 0.0000077 1.146 1.154 -0.65

1.377 0.320 129.200 708.661 0.001 0.0000088 1.242 1.270 -2.20

1.377 0.320 129.200 708.661 0.002 0.0000100 1.543 1.388 10.04

1.377 0.320 129.200 708.661 0.002 0.0000112 1.632 1.509 7.52

26

Figure-4.2.12 : CORRELATION PLOT OF BED FLUCTUATION RATIO AGAINST

SYSTEM PARAMETERS

� FOR EULER NUMBER (∆∆∆∆p/Uo2ρf)

y = 4452.x0.701

R² = 0.724

1

10

0.000001 0.00001 0.0001

r

e

x

p

t

product

( )292.1078.0

021.0

084.0076.0

4452

−×=

−

c

p

f

s

c

s

mf

mfo

D

dN

D

H

U

UUr

ρ

ρ

4.2.3 FOR Euler’s Number


Uavg/Umf Euler No

1.122241 867923

1.829655 530659.4

2.537068 387169.1

3.244482 278301.4

Hs/Dc Euler No

3.2 1018858

4.4 943386.6

5 1132064

5.6 698106.1

100000

1000000

E

u

l

e

r

N

o

100000

1000000

10000000

E

u

l

e

r

N

o

E.N Vs Uavg/Umf

E.N Vs Hs/Dc

27

FOR Euler’s Number


Figure-4.2.13 : E.N Vs Uavg/Umf

Figure-4.2.14 : E.N Vs Hs/Dc

y = 99344x

100000

1000000

1 Uavg/Umf

y = 2E+06x-0.41

100000

1000000

10000000

1

Hs/Dc

E.N = 99344 (Uavg/Umf )-1.05

E.N = 2E+06(Hs/Dc)-0.41

y = 99344x-1.05

10

10

1.05

28

N Euler No

73.9 1226403

101.6 1264138

121.2 1018858

137.4 867915.7

Figure-4.2.15 : E.N Vs N

ρs/ρf Euler

No

708.66

14

101885

8

2968.5

04

283016

0

2519.6

85

462259

5

4094.4

88

424524

0

y = 1E+07x-0.53

100000

1000000

10000000

10 100 1000

E

u

l

e

r

N

o

N

y = 4698.x0.829

1000000

10000000

100 1000 10000

E

u

l

e

r

N

o

ρs/ρf

E.N= 1E+07N-0.53

E.N Vs N

E.N = 4698(ρs/ρf )

0.829

E.N. Vs (ρs/ρf)

Figure-4.2.16 : E.N Vs (ρs/ρf)

29

dp/Dc Euler

No

0.0013 101885

8

0.0014 863433

0.0015 845274

0.0016 698106

.1

Figure-4.2.17 : E.N Vs (dp/Dc)

y = 15.73x-1.66

100000

1000000

10000000

0.001 0.01

E

u

l

e

r

N

o

dp/Dc

E.N = 15.73(dp/Dc)-1.66

E.N Vs (dp/Dc)

30

Table 4 - Observed Data & Comparison of Calculated Value of Euler Number ‘EN’

With Experimental ‘EN’ Value

Uavg/Umf Hs/Dc N, rpm ρs/ρf dp/Dc product E No.exp E No. cal %dev

1.122 3.200 137.400 708.661 0.001 576810.103 867923.002 951521.999 -9.63

1.830 3.200 137.400 708.661 0.001 345251.615 530659.444 547467.842 -3.17

2.537 3.200 137.400 708.661 0.001 244948.358 387169.131 378285.519 2.29

3.244 3.200 137.400 708.661 0.001 189199.798 278301.397 286437.587 -2.92

1.122 3.200 121.200 708.661 0.001 616466.439 1018857.575 1022160.066 -0.32

1.122 4.400 121.200 708.661 0.001 541010.049 943386.643 888072.839 5.86

1.122 5.600 121.200 708.661 0.001 490076.455 698106.116 798363.363 -14.36

1.122 3.200 73.900 708.661 0.001 801279.948 1226402.636 1355695.357 -10.54

1.122 3.200 101.600 708.661 0.001 676880.747 1264138.102 1130441.371 10.58

1.122 3.200 121.200 708.661 0.001 616466.439 1018857.575 1022160.066 -0.32

1.122 3.200 137.400 708.661 0.001 576810.103 867915.712 951521.999 -9.63

1.122 3.200 121.200 708.661 0.001 616466.439 1018857.575 1022160.066 -0.32

1.122 3.200 121.200 2968.504 0.002 1593910.208 2830159.930 2843413.452 -0.47

1.122 3.200 121.200 708.661 0.001 616466.439 1018857.575 1022160.066 -0.32

1.122 3.200 121.200 708.661 0.001 545108.387 863433.000 895320.419 -3.69

1.122 3.200 121.200 708.661 0.002 486120.474 845274.000 791424.771 6.37

1.122 3.200 121.200 708.661 0.002 436733.224 698106.116 705178.929 -1.01

31

Figure-4.2.13 : CORRELATION PLOT OF EULER NUMBER AGAINST SYSTEM

PARAMETERS

y = 0.594x1.077

R² = 0.944

100000

1000000

10000000

100000 1000000 10000000

E

N

e

x

p

t

PRODUCT

( )788.1893.0

571.0

442.0131.1

2594.0

−

−

−−

×=

∆

c

p

f

s

c

s

mffD

dN

D

H

U

Uavg

U

P

ρ

ρ

ρ

32

4.3 FINAL RESULTS

The correlations developed from the observed experimental data are as follows.

( )4064.2246.0

042.0

971.0083.0

066

−−

−

−

−×−=

c

p

f

s

c

s

mf

mfo

D

dN

D

H

U

UUER

ρ

ρ (2)

( )292.1078.0

021.0

084.0076.0

4452

−×=

−

c

p

f

s

c

s

mf

mfo

D

dN

D

H

U

UUr

ρ

ρ (3)

( )788.1893.0

571.0

442.0131.1

2594.0

−

−

−−

×=

∆

c

p

f

s

c

s

mffD

dN

D

H

U

Uavg

U

P

ρ

ρ

ρ (4)

33

4.4 DISCUSSION:

With different system parameters the dependent variables i.e. the fluidization characteristics such

as ‘R’ , ‘r’ & Euler’s No. vary differently. With increase in Uo (superficial velocity) both the

bed expansion and fluctuation ratios increase, but the Euler’s No. decreases with increase in Uo.

Again with increase in bed height (Hs) the bed expansion increases whereas the bed fluctuation

ratio and Euler’s Nos. are found to decrease. All the three dependent variables i.e ‘R’ , ‘r’ &

Euler’s No. are observed to be decreasing with the increased speed of the stirrer.

Apart from this it was also observed that sometimes the fluidization was not proper due to the

cohesive property of the particles. Special care should be taken while conducting the experiment

to prevent the excess fluctuation in bed pressure drop so as to get the proper fluidization.

The correlation obtained for bed expansion ratio (R) counts a deviation of +13 to -11%

between calculated and experimentally observed values which is reasonable. The correlation

obtained for bed fluctuation ratio (r) counts a deviation of +13 to -13% between calculated and

observed value . The correlation obtained for Euler’s No (∆p/Uo2ρf) counts a deviation of +10

to -14% between calculated and observed value of Euler Number. We can consider this

parameter for fluidization as these deviations are reasonable.

34

CHAPTER 5

Conclusion:

It was observed that the %deviation between the calculated and experimentally observed

values of bed expansion, bed fluctuation and Euler number are quite reasonable which indicates

the applicability of these developed correlations over a wide range of parameters. From the

developed correlation it was found that the expansion ratio ‘R’ increases with superficial velocity

Uo, but with other parameter i.e. static bed height (Hs),stirrer speed N ,particle density and

particle size dp it decreases. The fluctuation ratio ‘r’ decreases with increase speed of stirrer,but

with the remaining parameter it increases. The Euler No. found to decrease with all the

parameter except the particle density where it follows a reverse trend.

With the view of satisfactory fluidization achieved by using a stirrer in the fluidized bed, in

terms of obtained result, this method can be applicable in any industry with little medication as

per the requirement to perform in pilot scale where the fine particle can be efficiently handled.

The developed system can be used for drying of fine particles. This may also used in fluidized

bed reactor where catalysts are mainly smaller in size to provide large surface area for reaction to

occur. Apart from this, it can be used in pharmaceutical industry for different purposes. This

method can also be extended to nano scale where different mode of mechanical disturbance

such as vibration , rotating, use of sound amplifier may be use to break the cohesiveness of

particle. Further this method may be used in CFD analysis for different fluidization processes.

35

REFERENCE :

� Kumar A. Effects of Promoter & distributor parameter on the performance of gas-solid

fluidization, Ph. D Thesis, National Institute Of Technology , Rourkela (India),2003

� Wang Z.,Kwauk M.,Li H.Fluidization of fine particle,Chemical engg.

Science,53(1998)pp.377-395

� Xu C.,Zhu X-J.Effect of gas type on fine particle fluidization, CHINA

PARTICUOLOGY ,4( 2006) pp. 3-4, 114-121

� Watano S.,Nakamura H.,Hamada K. Fine particle coating by a novel rotating fluidized

bed coater, Powder Technology, 141(2004):pp.172-176

� Kumar A.,Roy G.K.Bed dynamics of gas-solid fluidized bed with rod promoter,China

particulogy,5(2007):pp.262-266

� Chirone R.,Russo S.Sound assisted fluidized bed combustion of fine particle,Combustion

Science and technology,153,pp.83-93

� Cardoso C.R., Ataide C.H., Abreu J.M. Minimum fluidization velocity of fine particle,

Material science forum,591(2008)pp.335-340

� Dave Rajesh.N, Yu Qun .Enhanced fluidization of nano particle in an oscillating

magnetic field, AICHE Journal , 51(2005):pp.1971-1977

� Liu Guangliang, Zhu Chao, Dave Rajesh.N . Sound assisted fluidization of nano

particle, Powder Technology 141(2004) 119-123

� Antonio Castellanos, Jose Manuel Valverde . Fluidization of nano particle:A simple

equation for estimating the size of agglomerate, Chemical engg., 140(2004) (296-304)

� Kunni D., Levenspeil O., Fluidization Engg., John Wiley,1961

36

APPENDIX

Material-Talcum Powder ( dp-65µm)

At-73.9 rpm

Flow

Rate

(lpm)

h1(cm) h2(cm) (h1-

h2)=B2-

C2

Usup(m/sec) del P Hmax(cm) Hmin(cm) r R

0 31 31 0 0 0 16 16 1 1

0.5 31.9 30 1.9 0.004244 295.279 16.2 16.2 1 1.0125

1 32.5 29.5 3 0.008489 466.2301 16.3 16.3 1 1.01875

2 33 29 4 0.016978 621.6401 25 23 1.086957 1.5

3 34.5 28 6.5 0.025467 1010.165 38 5 7.6 1.34375

4 34.8 27.5 7.3 0.033956 1134.493 41 38 1.078947 2.46875

5 35 27.2 7.8 0.042445 1212.198 44 40 1.1 2.625

6 35.2 27 8.2 0.050934 1274.362 48 40.5 1.185185 2.765625

7 35.3 26.9 8.4 0.059423 1305.444 49 41 1.195122 2.8125

8 35.5 26.8 8.7 0.067912 1352.067 50 42 1.190476 2.875

9 35.9 26.5 9.4 0.076401 1460.854 52 43 1.209302 2.96875

10 36 26.4 9.6 0.08489 1491.936 53 44 1.204545 3.03125

9 35.5 26.8 8.7 0.076401 1352.067 50 42 1.190476 2.875

8 35 27 8 0.067912 1243.28 49 41 1.195122 2.8125

7 34.9 27.2 7.7 0.059423 1196.657 46 40 1.15 2.6875

6 34.8 27.5 7.3 0.050934 1134.493 45 39 1.153846 2.625

5 34.5 27.8 6.7 0.042445 1041.247 42 37 1.135135 2.46875

4 34.4 28 6.4 0.033956 994.6241 41 36.5 1.123288 2.421875

3 34 28 6 0.025467 932.4601 40 36 1.111111 2.375

2 33.9 28.3 5.6 0.016978 870.2961 38 35 1.085714 2.28125

1 33.2 29 4.2 0.008489 652.7221 26 26 1 1.625

0.5 32.5 29.5 3 0.004244 466.2301 17 17 1 1.0625

0 31 31 0 0 0 16 16 1 1

37

At-101.6rpm

Flow h1(cm) h2(cm) (∆h) Usup(m/sec) ∆P (N/m2) Hmax(cm) Hmin(cm) r R

0 31 31 0 0 0 16 16 1 1

1 32.8 29.2 3.6 0.008489 559.4761 17 17 1 1.0625

2 34 28.5 5.5 0.016978 854.7551 34 33 1.030303 2.09375

3 34.5 27.8 6.7 0.025467 1041.247 39 34 1.147059 2.28125

4 34.6 27.5 7.1 0.033956 1103.411 41 37 1.108108 2.4375

5 35 27 8 0.042445 1243.28 42 38 1.105263 2.5

6 35.2 26.9 8.3 0.050934 1289.903 44 40 1.1 2.625

7 35.2 26.8 8.4 0.059423 1305.444 45 41 1.097561 2.6875

8 35.5 26.5 9 0.067912 1398.69 47 41 1.146341 2.75

9 35.8 26.2 9.6 0.076401 1491.936 49 41.5 1.180723 2.828125

10 36.2 25.9 10.3 0.08489 1600.723 50 42 1.190476 2.875

9 35.7 26.3 9.4 0.076401 1460.854 47 41 1.146341 2.75

8 35.5 26.8 8.7 0.067912 1352.067 45 40 1.125 2.65625

7 35 27 8 0.059423 1243.28 44 39 1.128205 2.59375

6 35 27.2 7.8 0.050934 1212.198 43 38 1.131579 2.53125

5 34.8 27.5 7.3 0.042445 1134.493 41 37 1.108108 2.4375

4 34.5 27.9 6.6 0.033956 1025.706 39 36 1.083333 2.34375

3 34.1 28 6.1 0.025467 948.0011 37 35.8 1.03352 2.275

2 34 28.1 5.9 0.016978 916.9191 36 34 1.058824 2.1875

1 33.8 28.5 5.3 0.008489 823.6731 31 30 1.033333 1.90625

0 31 31 0 0 0 16 16 1 1

38

At-121.2µm

Flow

Rate

(lpm)

h1(cm)

h2(cm)

(h1-

h2)

Usup(m/sec) ∆P

(N/m2)

Hmax(cm) Hmin(cm) r R

0 31.4 30 0 0 0 16 16 1 1

1 32.5 29 2.1 0.008489 326.361 18.5 18.5 1 1.15625

2 34 27.8 4.8 0.016978 745.9681 37 33.5 1.104478 2.203125

3 34.2 27.4 5.4 0.025467 839.2141 39 35 1.114286 2.3125

4 34.4 27 6 0.033956 932.4601 42 37 1.135135 2.46875

5 34.7 26.9 6.4 0.042445 994.6241 44 38 1.157895 2.5625

6 34.9 26.8 6.7 0.050934 1041.247 45.5 39 1.166667 2.640625

7 35 26.6 7 0.059423 1087.87 47 41 1.146341 2.75

8 35.2 26.4 7.4 0.067912 1150.034 48 41.5 1.156627 2.796875

9 35.4 26.2 7.8 0.076401 1212.198 49.5 42 1.178571 2.859375

10 35.6 26 8.2 0.08489 1274.362 50 42 1.190476 2.875

9 35.5 26.1 8 0.076401 1243.28 48 41.5 1.156627 2.796875

8 35.2 26.6 7.2 0.067912 1118.952 46.5 40 1.1625 2.703125

7 34.9 26.8 6.7 0.059423 1041.247 45 39 1.153846 2.625

6 34.8 26.9 6.5 0.050934 1010.165 43.5 37.5 1.16 2.53125

5 34.3 27.3 5.6 0.042445 870.2961 42 36.5 1.150685 2.453125

4 34.1 27.5 5.2 0.033956 808.1321 41 36 1.138889 2.40625

3 33.9 27.8 4.7 0.025467 730.4271 40 35 1.142857 2.34375

2 33.7 28 4.3 0.016978 668.2631 38 34 1.117647 2.25

1 33.4 28.2 3.8 0.008489 590.5581 29 29 1 1.8125

0 31.4 30 0 0 0 16 16 1 1

39

At 137.4 rpm

Flow Rate(lpm) h1(cm) h2(cm) (h1-h2) Usup(m/sec) ∆P

(N/m2)

Hmax(cm) Hmin(cm) r R

0 31.9 29.8 0 0 0 16 16 1 1

1 32 29.6 0.3 0.008489 46.62301 18 18 1 1.125

2 34.2 29 3.1 0.016978 481.7711 27 24 1.125 1.59375

3 34.2 27.5 4.6 0.025467 714.8861 41 35.5 1.15493 2.390625

4 34.3 27.2 5 0.033956 777.0501 43 38 1.131579 2.53125

5 34.8 27 5.7 0.042445 885.8371 45 39 1.153846 2.625

6 34.9 26.9 5.9 0.050934 916.9191 46 40 1.15 2.6875

7 35.2 26.5 6.6 0.059423 1025.706 47 40 1.175 2.71875

8 35.4 26.2 7.1 0.067912 1103.411 48 41 1.170732 2.78125

9 35.5 26 7.4 0.076401 1150.034 49 42 1.166667 2.84375

10 36.3 25.5 8.7 0.08489 1352.067 51 44 1.159091 2.96875

9 35.4 26.2 7.1 0.076401 1103.411 47 44 1.068182 2.84375

8 35 26.5 6.4 0.067912 994.6241 45 40 1.125 2.65625

7 34.9 26.9 5.9 0.059423 916.9191 44 39.5 1.113924 2.609375

6 34.6 27 5.5 0.050934 854.7551 43 39 1.102564 2.5625

5 34.4 27.2 5.1 0.042445 792.5911 41 38 1.078947 2.46875

4 34.2 27.5 4.6 0.033956 714.8861 40 37 1.081081 2.40625

3 34 27.8 4.1 0.025467 637.1811 39 36 1.083333 2.34375

2 33.8 28 3.7 0.016978 575.0171 37 35 1.057143 2.25

1 33.4 28.2 3.1 0.008489 481.7711 33 33 1 2.0625

0 31.9 29.8 0 0 0 16 16 1 1

40

Hs=22cm.At-121.2rpm

Flow

Rate(lpm

)

h1(cm) h2(cm) (h1-h2) Usup(m/sec

)

del P Hmax(cm

)

Hmin(cm

)

r R

0 28 27.5 0 0 0 22 22 1 1.375

1 29 26.5 2 0.008489 310.82 24 24 1 1.5

2 30 26 3.5 0.016978 543.9351 24.5 24.5 1 1.53125

3 30.5 25 5 0.025467 777.0501 27 24.5 1.102041 1.609375

4 31 24.5 6 0.033956 932.4601 30 25 1.2 1.71875

5 32 24 7.5 0.042445 1165.575 31 25 1.24 1.75

6 32.5 23 9 0.050934 1398.69 36 32 1.125 2.125

7 33 22.5 10 0.059423 1554.1 39 33 1.181818 2.25

8 33.5 22 11 0.067912 1709.51 44 35 1.257143 2.46875

9 34 21 12.5 0.076401 1942.625 53 42 1.261905 2.96875

10 35 20.5 14 0.08489 2175.74 57 49 1.163265 3.3125

9 33.5 21 12 0.076401 1864.92 53 47 1.12766 3.125

8 32.5 23 9 0.067912 1398.69 50 46 1.086957 3

7 32 23.5 8 0.059423 1243.28 49 44 1.113636 2.90625

6 31.5 24 7 0.050934 1087.87 47 43 1.093023 2.8125

5 31 24 6.5 0.042445 1010.165 46 43 1.069767 2.78125

4 31 24.5 6 0.033956 932.4601 45 41 1.097561 2.6875

3 30 25 4.5 0.025467 699.3451 35 31 1.129032 2.0625

2 30 26 3.5 0.016978 543.9351 30 27 1.111111 1.78125

1 29 26.5 2 0.008489 310.82 24.5 24.5 1 1.53125

0 28 27.5 0 0 0 22 22 1 1.375

41

At Hs-25cm.121.2rpm

Flow

Rate(lpm

h1(cm) h2(cm) (h1-h2) Usup(m/sec) del P Hmax(cm

)

Hmin(cm

)

r R

0 28 27.5 0 0 0 25 25 1 1.5625

1 29 26.5 2 0.008489 310.82 26 26 1 1.625

2 30.5 25 5 0.016978 777.0501 31 27 1.148148 1.8125

3 31 24.5 6 0.025467 932.4601 32 28 1.142857 1.875

4 31.5 24 7 0.033956 1087.87 33 28 1.178571 1.90625

5 32 23 8.5 0.042445 1320.985 34 28.5 1.192982 1.953125

6 32 23 8.5 0.050934 1320.985 35 29 1.206897 2

7 32.5 22.5 9.5 0.059423 1476.395 36 30 1.2 2.0625

8 33 22 10.5 0.067912 1631.805 38 30 1.266667 2.125

9 34 21 12.5 0.076401 1942.625 39 31 1.258065 2.1875

10 35 20 14.5 0.08489 2253.445 56 46 1.217391 3.1875

9 34 21.5 12 0.076401 1864.92 53 46 1.152174 3.09375

8 33 22 10.5 0.067912 1631.805 51 46 1.108696 3.03125

7 32.5 22.5 9.5 0.059423 1476.395 50 45 1.111111 2.96875

6 32.5 23 9 0.050934 1398.69 49 44 1.113636 2.90625

5 31.5 24.5 6.5 0.042445 1010.165 46 43 1.069767 2.78125

4 31 25 5.5 0.033956 854.7551 44 41 1.073171 2.65625

3 30.5 25 5 0.025467 777.0501 42 39 1.076923 2.53125

2 30 26 3.5 0.016978 543.9351 35 32 1.09375 2.09375

1 29 27 1.5 0.008489 233.115 29 29 1 1.8125

0 28 27.5 0 0 0 27 27 1 1.6875

42

At Hs-28cm,121.2rpm

Flow

Rate(lpm


)

del P Hmax(cm

)

Hmin(cm

)

r R

0 34.2 33.5 2.88658E-15 0 4.49E-13 28 28 1 1

1 34.5 33.4 0.4 0.008489 62.16401 30 30 1 1.071429

2 36 32 3.3 0.016978 512.8531 30.5 30.5 1 1.089286

3 36.2 31.8 3.7 0.025467 575.0171 31 31 1 1.107143

4 36.5 31.5 4.3 0.033956 668.2631 37 31.5 1.174603 1.223214

5 36.8 31.2 4.9 0.042445 761.5091 38 32 1.1875 1.25

6 37 31 5.3 0.050934 823.6731 39 32.5 1.2 1.276786

7 37.2 30.8 5.7 0.059423 885.8371 40 32.5 1.230769 1.294643

8 37.3 30.5 6.1 0.067912 948.0011 41 32.5 1.261538 1.3125

9 37.5 30.5 6.3 0.076401 979.0831 43 32.5 1.323077 1.348214

10 37.5 30.5 6.3 0.08489 979.0831 48 33 1.454545 1.446429

9 37.5 30.5 6.3 0.076401 979.0831 45 33 1.363636 1.392857

8 37.2 30.7 5.8 0.067912 901.3781 44 33 1.333333 1.375

7 37 31 5.3 0.059423 823.6731 40 32 1.25 1.285714

6 36.8 31.1 5 0.050934 777.0501 40 32 1.25 1.285714

5 36.5 31.8 4 0.042445 621.6401 38 32 1.1875 1.25

4 36.2 32 3.5 0.033956 543.9351 36 31 1.16129 1.196429

3 36 33 2.3 0.025467 357.443 34 30.5 1.114754 1.151786

2 35 33.5 0.8 0.016978 124.328 30 30 1 1.071429

1 34.5 33.5 0.3 0.008489 46.62301 29 29 1 1.035714

0 34.2 33.5 2.88658E-15 0 4.49E-13 28 28 1 1

43

Talcum Powder ( dp-80µm)

At 73.9 rpm,Hs-16cm

Flow

Rate(lpm


)

∆P

(N/m2)

Hmax(cm

)

Hmin(cm

)

r R

0 36.5 37 0 0 0 16 16 1 1

1 37.5 36 2 0.008489 310.82 16.2 16.2 1 1.0125

2 38.1 35.5 3.1 0.016978 481.7711 17 17 1 1.0625

3 38.5 35 4 0.025467 621.6401 19 17.5 1.085714 1.140625

4 38.8 34.5 4.8 0.033956 745.9681 21 18 1.166667 1.21875

5 39.2 34.3 5.4 0.042445 839.2141 26 18.5 1.405405 1.390625

6 39.5 34 6 0.050934 932.4601 27 19 1.421053 1.4375

7 40 33.5 7 0.059423 1087.87 29 20 1.45 1.53125

8 40 33.5 7 0.067912 1087.87 30 20 1.5 1.5625

9 40.4 33 7.9 0.076401 1227.739 31 21 1.47619 1.625

10 41 32.5 9 0.08489 1398.69 31 21 1.47619 1.625

9 40.4 33 7.9 0.076401 1227.739 30 20.5 1.463415 1.578125

8 40 33.5 7 0.067912 1087.87 28 20 1.4 1.5

7 39.5 34 6 0.059423 932.4601 26 19 1.368421 1.40625

6 39 34.3 5.2 0.050934 808.1321 24 18.5 1.297297 1.328125

5 38.7 34.8 4.4 0.042445 683.8041 23 18 1.277778 1.28125

4 38.2 35 3.7 0.033956 575.0171 22 17.5 1.257143 1.234375

3 38 35.5 3 0.025467 466.2301 20 17 1.176471 1.15625

2 37.9 35.8 2.6 0.016978 404.0661 18 17 1.058824 1.09375

1 37 36.5 1 0.008489 155.41 17 17 1 1.0625

44

At 101.6rpm

Flow

Rate(lpm

h1(cm) h2(cm) (h1-h2) Usup(m/sec) ∆P

(N/m2)

Hmax(cm

)

Hmin(cm

)

r R

0 36.5 37 0 0 0 16 16 1 1

1 37.5 36 2 0.008489 310.82 17 17 1 1.0625

2 38.3 35.5 3.3 0.016978 512.8531 19 17.5 1.085714 1.140625

3 38.5 35 4 0.025467 621.6401 21 18 1.166667 1.21875

4 39 34.5 5 0.033956 777.0501 23 18 1.277778 1.28125

5 39.2 34.2 5.5 0.042445 854.7551 25 19 1.315789 1.375

6 39.5 33.8 6.2 0.050934 963.5421 29 19 1.526316 1.5

7 40 33.5 7 0.059423 1087.87 30 19 1.578947 1.53125

8 40.3 33 7.8 0.067912 1212.198 31 19 1.631579 1.5625

9 40.5 33 8 0.076401 1243.28 32 19 1.684211 1.59375

10 41.5 32.5 9.5 0.08489 1476.395 32 19 1.684211 1.59375

9 40.5 33 8 0.076401 1243.28 31 19 1.631579 1.5625

8 40 33.5 7 0.067912 1087.87 30 19 1.578947 1.53125

7 39.8 34 6.3 0.059423 979.0831 30 19 1.578947 1.53125

6 39.2 34 5.7 0.050934 885.8371 29 19 1.526316 1.5

5 39 34.5 5 0.042445 777.0501 28 18.5 1.513514 1.453125

4 38.5 34.8 4.2 0.033956 652.7221 26 18 1.444444 1.375

3 38.3 35.2 3.6 0.025467 559.4761 23 18 1.277778 1.28125

2 38 35.5 3 0.016978 466.2301 20 17 1.176471 1.15625

1 37.5 36 2 0.008489 310.82 17 17 1 1.0625

0 36.5 37 0 0 0 16 16 1 1

45

At 121.2rpm-

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36.5 37 0 0 0 16 16 1 1

1 37.2 36 1.7 0.008489 264.197 17 17 1 1.0625

2 38 35.5 3 0.016978 466.2301 23 17 1.352941 1.25

3 38.2 35 3.7 0.025467 575.0171 25 17.5 1.428571 1.328125

4 38.6 34.8 4.3 0.033956 668.2631 28 18 1.555556 1.4375

5 39 34.2 5.3 0.042445 823.6731 29 18 1.611111 1.46875

6 39.4 34 5.9 0.050934 916.9191 30 18.5 1.621622 1.515625

7 39.6 33.6 6.5 0.059423 1010.165 31 19 1.631579 1.5625

8 40 33 7.5 0.067912 1165.575 32 19 1.684211 1.59375

9 40.3 32.8 8 0.076401 1243.28 33 19 1.736842 1.625

10 41 31.5 10 0.08489 1554.1 33 19 1.736842 1.625

9 40 32.8 7.7 0.076401 1196.657 31 19 1.631579 1.5625

8 40 33 7.5 0.067912 1165.575 29 19 1.526316 1.5

7 39.5 34 6 0.059423 932.4601 28 19 1.473684 1.46875

6 39 34 5.5 0.050934 854.7551 27 18 1.5 1.40625

5 38.8 34.3 5 0.042445 777.0501 25 18 1.388889 1.34375

4 38.5 35 4 0.033956 621.6401 24 17.5 1.371429 1.296875

3 38 35.2 3.3 0.025467 512.8531 23 17.5 1.314286 1.265625

2 37.5 35.5 2.5 0.016978 388.5251 22 17 1.294118 1.21875

1 37.6 36 2.1 0.008489 326.361 19 16.5 1.151515 1.109375

0 36.5 37 0 0 0 16 16 1 1

46

At 137.4rpm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36.5 37 0 0 0 16 16 1 1

1 37.2 36 1.7 0.008489 264.197 16.5 16.5 1 1.03125

2 38 35 3.5 0.016978 543.9351 24 17 1.411765 1.28125

3 38.5 35 4 0.025467 621.6401 28 17.5 1.6 1.421875

4 39 34.5 5 0.033956 777.0501 29 18 1.611111 1.46875

5 39 34 5.5 0.042445 854.7551 29 18 1.611111 1.46875

6 39.5 34 6 0.050934 932.4601 30 18.5 1.621622 1.515625

7 40 33.5 7 0.059423 1087.87 30 18.5 1.621622 1.515625

8 40.3 33 7.8 0.067912 1212.198 31 18.5 1.675676 1.546875

9 41 32.5 9 0.076401 1398.69 31 19 1.631579 1.5625

10 42 31 11.5 0.08489 1787.215 31 20 1.55 1.59375

9 40.5 32.5 8.5 0.076401 1320.985 30 19.5 1.538462 1.546875

8 40 33 7.5 0.067912 1165.575 29 19 1.526316 1.5

7 39.5 33.5 6.5 0.059423 1010.165 26 18.5 1.405405 1.390625

6 39 34 5.5 0.050934 854.7551 25 18 1.388889 1.34375

5 39 34.3 5.2 0.042445 808.1321 25 17.5 1.428571 1.328125

4 38.5 35 4 0.033956 621.6401 24 17 1.411765 1.28125

3 38 35.5 3 0.025467 466.2301 22 17 1.294118 1.21875

2 37.7 35.8 2.4 0.016978 372.984 22 16.5 1.333333 1.203125

1 37.5 36 2 0.008489 310.82 20 16 1.25 1.125

0 36.5 37 0 0 0 16 16 1 1

47

At Hs-18cm,121.2 rpm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36.5 37 0 0 0 18 18 1 1

1 38 35.5 3 0.008489 466.2301 23 18 1.277778 1.138889

2 38.3 35.2 3.6 0.016978 559.4761 23.5 18.5 1.27027 1.166667

3 39 34.5 5 0.025467 777.0501 24 18.5 1.297297 1.180556

4 39.3 34 5.8 0.033956 901.3781 25 19 1.315789 1.222222

5 39.8 33.5 6.8 0.042445 1056.788 26 19.5 1.333333 1.263889

6 40 33 7.5 0.050934 1165.575 27 19.5 1.384615 1.291667

7 40.2 33 7.7 0.059423 1196.657 31 20 1.55 1.416667

8 40.5 32.8 8.2 0.067912 1274.362 33 20 1.65 1.472222

9 41 32.2 9.3 0.076401 1445.313 37 20 1.85 1.583333

10 42 31.8 10.7 0.08489 1662.887 37 20 1.85 1.583333

9 41 32.8 8.7 0.076401 1352.067 32 20 1.6 1.444444

8 40.8 33 8.3 0.067912 1289.903 31 20 1.55 1.416667

7 40 33.5 7 0.059423 1087.87 30 20 1.5 1.388889

6 39.5 34 6 0.050934 932.4601 29 20 1.45 1.361111

5 39.3 34 5.8 0.042445 901.3781 27 20 1.35 1.305556

4 39 34.5 5 0.033956 777.0501 26 20 1.3 1.277778

3 38.5 35 4 0.025467 621.6401 23 19 1.210526 1.166667

2 38 35.3 3.2 0.016978 497.3121 22 19 1.157895 1.138889

1 37.5 36 2 0.008489 310.82 19.5 19 1.026316 1.069444

0 36.5 37 0 0 0 18 18 1 1

48

At Hs-21cm,121.2rpm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36.5 37 0 0 0 21 21 1 1

1 38 35.8 2.7 0.008489 419.6071 22 21 1.047619 1.02381

2 38.5 35 4 0.016978 621.6401 23 21 1.095238 1.047619

3 39 34.5 5 0.025467 777.0501 24 21 1.142857 1.071429

4 39 34 5.5 0.033956 854.7551 26 21 1.238095 1.119048

5 39.5 33.8 6.2 0.042445 963.5421 27 21.5 1.255814 1.154762

6 40 33.5 7 0.050934 1087.87 27 22 1.227273 1.166667

7 40.2 33 7.7 0.059423 1196.657 27 22 1.227273 1.166667

8 40.2 33 7.7 0.067912 1196.657 29 22 1.318182 1.214286

9 41 32 9.5 0.076401 1476.395 31 23 1.347826 1.285714

10 42.5 30.5 12.5 0.08489 1942.625 32 23 1.391304 1.309524

9 40.5 33 8 0.076401 1243.28 30 22 1.363636 1.238095

8 40.2 33 7.7 0.067912 1196.657 29 22 1.318182 1.214286

7 40 33.5 7 0.059423 1087.87 28 21.5 1.302326 1.178571

6 39.2 34 5.7 0.050934 885.8371 26 21 1.238095 1.119048

5 39 34.2 5.3 0.042445 823.6731 26 21 1.238095 1.119048

4 38.5 34.5 4.5 0.033956 699.3451 25 21 1.190476 1.095238

3 38 35.3 3.2 0.025467 497.3121 24 21 1.142857 1.071429

2 38 35.5 3 0.016978 466.2301 23 21 1.095238 1.047619

1 37.2 36 1.7 0.008489 264.197 21 21 1 1

0 36.5 37 0 0 0 21 21 1 1

49

Material-Alumina Powder (dp-75µm)

Hs-16cm,73.9rpm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36.5 36 0 0 0 16 16 1 1

1 42 29 12.5 0.008489 1942.625 19.5 18.5 1.054054 1.1875

2 43 28.5 14 0.016978 2175.74 22 20 1.1 1.3125

3 43.3 28.2 14.6 0.025467 2268.986 23 20.5 1.121951 1.359375

4 43.5 28 15 0.033956 2331.15 25 21 1.190476 1.4375

5 44 28 15.5 0.042445 2408.855 25 21 1.190476 1.4375

6 44.2 27.5 16.2 0.050934 2517.642 27 22 1.227273 1.53125

7 44.3 27.5 16.3 0.059423 2533.183 28 22 1.272727 1.5625

8 45 27 17.5 0.067912 2719.675 30 22 1.363636 1.625

9 45 26.5 18 0.076401 2797.38 32 22 1.454545 1.6875

10 47.5 24 23 0.08489 3574.43 41 23 1.782609 2

9 44.5 27 17 0.076401 2641.97 33 22 1.5 1.71875

8 44 27.5 16 0.067912 2486.56 30 22 1.363636 1.625

7 44 27.5 16 0.059423 2486.56 29 22 1.318182 1.59375

6 44 28 15.5 0.050934 2408.855 28 21.5 1.302326 1.546875

5 44 28 15.5 0.042445 2408.855 27 21 1.285714 1.5

4 43.5 28.5 14.5 0.033956 2253.445 25 21 1.190476 1.4375

3 43 29 13.5 0.025467 2098.035 23 20 1.15 1.34375

2 43 29 13.5 0.016978 2098.035 21 20 1.05 1.28125

1 42 29.5 12 0.008489 1864.92 17 17 1 1.0625

50

At 101.6 rpm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36.2 35.8 5.66E-15 0 8.8E-13 16 16 1 1

1 42.5 29 13.1 0.008489 2035.871 17 17 1 1.0625

2 42.5 29 13.1 0.016978 2035.871 24 20 1.2 1.375

3 43.2 28.5 14.3 0.025467 2222.363 25 20 1.25 1.40625

4 43.5 28 15.1 0.033956 2346.691 26 21 1.238095 1.46875

5 44 28 15.6 0.042445 2424.396 27 21 1.285714 1.5

6 44 28 15.6 0.050934 2424.396 28 21.5 1.302326 1.546875

7 44.5 27.5 16.6 0.059423 2579.806 30 22 1.363636 1.625

8 44.5 27 17.1 0.067912 2657.511 31 22 1.409091 1.65625

9 45 27 17.6 0.076401 2735.216 32 22 1.454545 1.6875

10 45.5 26.5 18.6 0.08489 2890.626 32 22.5 1.422222 1.703125

9 45 27 17.6 0.076401 2735.216 31 22 1.409091 1.65625

8 44.5 27 17.1 0.067912 2657.511 31 22 1.409091 1.65625

7 44 27.5 16.1 0.059423 2502.101 30 22 1.363636 1.625

6 44 28 15.6 0.050934 2424.396 29 21.5 1.348837 1.578125

5 44 28 15.6 0.042445 2424.396 27 21 1.285714 1.5

4 43.5 28.5 14.6 0.033956 2268.986 25 21 1.190476 1.4375

3 43 29 13.6 0.025467 2113.576 24 20 1.2 1.375

2 43 29 13.6 0.016978 2113.576 22 20 1.1 1.3125

1 42.5 29.5 12.6 0.008489 1958.166 18 18 1 1.125

0 36.2 35.8 5.66E-15 0 8.8E-13 16 16 1 1

51

At 121.2rpm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36 36 0 0 0 16 16 1 1

1 42.5 29 13.5 0.008489 2098.035 17 17 1 1.0625

2 43.2 28.8 14.4 0.016978 2237.904 22 20 1.1 1.3125

3 43.5 28.5 15 0.025467 2331.15 24 20.5 1.170732 1.390625

4 43.5 28 15.5 0.033956 2408.855 25 21 1.190476 1.4375

5 44 28 16 0.042445 2486.56 27 21 1.285714 1.5

6 44 28 16 0.050934 2486.56 28 21 1.333333 1.53125

7 44.5 27.5 17 0.059423 2641.97 30 22 1.363636 1.625

8 44.5 27 17.5 0.067912 2719.675 32 22 1.454545 1.6875

9 45 27 18 0.076401 2797.38 33 22 1.5 1.71875

10 45 26.5 18.5 0.08489 2875.085 36 22 1.636364 1.8125

9 44.5 27 17.5 0.076401 2719.675 32 22 1.454545 1.6875

8 44 27.5 16.5 0.067912 2564.265 31 22 1.409091 1.65625

7 44 28 16 0.059423 2486.56 30 22 1.363636 1.625

6 44 28 16 0.050934 2486.56 29 21 1.380952 1.5625

5 44 28 16 0.042445 2486.56 27 21 1.285714 1.5

4 43.5 28 15.5 0.033956 2408.855 25 21 1.190476 1.4375

3 43.2 28.5 14.7 0.025467 2284.527 22 21 1.047619 1.34375

2 43 29 14 0.016978 2175.74 21 20 1.05 1.28125

1 42 30 12 0.008489 1864.92 17 17 1 1.0625

0 36 36 0 0 0 16 16 1 1

52

At 137.4rpm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36 36 0 0 0 16 16 1 1

1 43 29 14 0.008489 2175.74 19 18 1.055556 1.15625

2 43 29 14 0.016978 2175.74 22 19 1.157895 1.28125

3 43.2 28.5 14.7 0.025467 2284.527 24 20 1.2 1.375

4 43.5 28.5 15 0.033956 2331.15 25 21 1.190476 1.4375

5 44 28 16 0.042445 2486.56 26 21 1.238095 1.46875

6 44 28 16 0.050934 2486.56 27 21.5 1.255814 1.515625

7 44.5 27.5 17 0.059423 2641.97 29 22 1.318182 1.59375

8 45 27 18 0.067912 2797.38 31 22 1.409091 1.65625

9 45 27 18 0.076401 2797.38 33 22.5 1.466667 1.734375

10 45.5 26.5 19 0.08489 2952.79 36 23 1.565217 1.84375

9 45 27 18 0.076401 2797.38 31 22 1.409091 1.65625

8 44.5 27.5 17 0.067912 2641.97 30 22 1.363636 1.625

7 44 28 16 0.059423 2486.56 28 21 1.333333 1.53125

6 44 28 16 0.050934 2486.56 27 21 1.285714 1.5

5 44 28 16 0.042445 2486.56 25 21 1.190476 1.4375

4 43.5 28.5 15 0.033956 2331.15 24 21 1.142857 1.40625

3 43 29 14 0.025467 2175.74 23 20 1.15 1.34375

2 43 29 14 0.016978 2175.74 22 20 1.1 1.3125

1 42.5 29.5 13 0.008489 2020.33 17 17 1 1.0625

0 36 36 0 0 0 16 16 1 1

53

At Hs-18cm,121.2rpm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36 36 0 0 0 18 18 1 1

1 44 28 16 0.008489 2486.56 22 22 1 1.222222

2 44.5 27.5 17 0.016978 2641.97 27.5 24 1.145833 1.430556

3 44.5 27.5 17 0.025467 2641.97 29 24 1.208333 1.472222

4 45 27 18 0.033956 2797.38 31 24 1.291667 1.527778

5 45 27 18 0.042445 2797.38 32 25 1.28 1.583333

6 45.5 26.5 19 0.050934 2952.79 32 25 1.28 1.583333

7 45.5 26.5 19 0.059423 2952.79 33 26 1.269231 1.638889

8 46 26 20 0.067912 3108.2 36 26 1.384615 1.722222

9 46 26 20 0.076401 3108.2 39 26 1.5 1.805556

10 47 25 22 0.08489 3419.02 41 27 1.518519 1.888889

9 46 26 20 0.076401 3108.2 36 27 1.333333 1.75

8 45.5 26.5 19 0.067912 2952.79 35 26 1.346154 1.694444

7 45.5 26.5 19 0.059423 2952.79 33 26 1.269231 1.638889

6 45 27 18 0.050934 2797.38 32 25 1.28 1.583333

5 44.5 27 17.5 0.042445 2719.675 31 25 1.24 1.555556

4 44.5 27.5 17 0.033956 2641.97 30 24 1.25 1.5

3 44 27.5 16.5 0.025467 2564.265 29 24 1.208333 1.472222

2 44 28 16 0.016978 2486.56 27 24 1.125 1.416667

1 44 28 16 0.008489 2486.56 21 21 1 1.166667

0 36 36 0 0 0 18 18 1 1

54

At Hs-21cm,12.2rpm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36 36 0 0 0 21 21 1 1

1 45 27.5 17.5 0.008489 2719.675 24 24 1 1.142857

2 45 27 18 0.016978 2797.38 31 26 1.192308 1.357143

3 45.5 26.8 18.7 0.025467 2906.167 32 26 1.230769 1.380952

4 45.5 26.5 19 0.033956 2952.79 32 26 1.230769 1.380952

5 46 26 20 0.042445 3108.2 33 27 1.222222 1.428571

6 46 26 20 0.050934 3108.2 34 27 1.259259 1.452381

7 46.5 26 20.5 0.059423 3185.905 36 28 1.285714 1.52381

8 46.5 25.5 21 0.067912 3263.61 41 28 1.464286 1.642857

9 47 25 22 0.076401 3419.02 41 29 1.413793 1.666667

10 47.5 24.5 23 0.08489 3574.43 42 30 1.4 1.714286

9 46.5 25 21.5 0.076401 3341.315 39 29 1.344828 1.619048

8 46.5 25 21.5 0.067912 3341.315 38 28 1.357143 1.571429

7 46.5 25.5 21 0.059423 3263.61 37 28 1.321429 1.547619

6 46 26 20 0.050934 3108.2 35 27 1.296296 1.47619

5 46 26 20 0.042445 3108.2 33 27 1.222222 1.428571

4 45.5 26.5 19 0.033956 2952.79 33 26.5 1.245283 1.416667

3 45 27 18 0.025467 2797.38 30 26 1.153846 1.333333

2 45 27.5 17.5 0.016978 2719.675 30 26 1.153846 1.333333

1 44 28 16 0.008489 2486.56 22 22 1 1.047619

0 36 36 0 0 0 21 21 1 1

55

Material-Silicon Carbide (dp-70µm)

At 73.9rpm,Hs-16cm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36 36 0 0 0 16 16 1 1

1 43.5 28 15.5 0.008489 2408.855 17 17 1 1.0625

2 47.5 24 23.5 0.016978 3652.135 20 20 1 1.25

3 48 23 25 0.025467 3885.251 23 21 1.095238 1.375

4 48.5 22.5 26 0.033956 4040.661 27 21.5 1.255814 1.515625

5 49 22 27 0.042445 4196.071 29 22 1.318182 1.59375

6 49 22 27 0.050934 4196.071 30 22.5 1.333333 1.640625

7 49.5 21.5 28 0.059423 4351.481 32 22.5 1.422222 1.703125

8 50 21 29 0.067912 4506.891 34 23 1.478261 1.78125

9 51 20.5 30.5 0.076401 4740.006 36 24 1.5 1.875

10 52 20 32 0.08489 4973.121 39 25 1.56 2

9 50 21 29 0.076401 4506.891 35 24 1.458333 1.84375

8 49.5 21.5 28 0.067912 4351.481 32 23 1.391304 1.71875

7 49 22 27 0.059423 4196.071 31 23 1.347826 1.6875

6 49 22 27 0.050934 4196.071 31 22.5 1.377778 1.671875

5 48.5 23 25.5 0.042445 3962.956 29 22 1.318182 1.59375

4 48.5 23 25.5 0.033956 3962.956 25 21 1.190476 1.4375

3 47.5 24 23.5 0.025467 3652.135 23 21 1.095238 1.375

2 47.5 24 23.5 0.016978 3652.135 21 20 1.05 1.28125

1 41.5 30 11.5 0.008489 1787.215 18 18 1 1.125

56

At 101.6 rpm, Hs-16cm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36 36 0 0 0 16 16 1 1

1 42.5 29 13.5 0.008489 2098.035 16.5 16.5 1 1.03125

2 47 24 23 0.016978 3574.43 20 19 1.052632 1.21875

3 48 23.5 24.5 0.025467 3807.545 22 20 1.1 1.3125

4 48.5 23 25.5 0.033956 3962.956 24 21 1.142857 1.40625

5 49 22.5 26.5 0.042445 4118.366 26 21.5 1.209302 1.484375

6 49.5 22 27.5 0.050934 4273.776 29 22 1.318182 1.59375

7 50 22 28 0.059423 4351.481 30 22.5 1.333333 1.640625

8 50.5 21 29.5 0.067912 4584.596 31 23 1.347826 1.6875

9 50.5 21 29.5 0.076401 4584.596 32 23 1.391304 1.71875

10 53 19 34 0.08489 5283.941 37 25 1.48 1.9375

9 50 21.5 28.5 0.076401 4429.186 32 23 1.391304 1.71875

8 49.5 22 27.5 0.067912 4273.776 31 23 1.347826 1.6875

7 49 22 27 0.059423 4196.071 29 22 1.318182 1.59375

6 49 22 27 0.050934 4196.071 28 22 1.272727 1.5625

5 48 23 25 0.042445 3885.251 25 21 1.190476 1.4375

4 48 23 25 0.033956 3885.251 23 21 1.095238 1.375

3 47.5 24 23.5 0.025467 3652.135 22 20.5 1.073171 1.328125

2 47.5 29 18.5 0.016978 2875.085 19 19 1 1.1875

1 42 29.5 12.5 0.008489 1942.625 17.5 17.5 1 1.09375

0 36 36 0 0 0 16 16 1 1

57

At-121.2rpm,Hs-16cm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36 36 0 0 0 16 16 1 1

1 43 29 14 0.008489 2175.74 17 17 1 1.0625

2 47.5 23.5 24 0.016978 3729.84 21 20 1.05 1.28125

3 48 23.5 24.5 0.025467 3807.545 22 20 1.1 1.3125

4 48.5 23 25.5 0.033956 3962.956 24 21 1.142857 1.40625

5 49 22.5 26.5 0.042445 4118.366 25 21 1.190476 1.4375

6 50 22 28 0.050934 4351.481 29 22 1.318182 1.59375

7 50 22 28 0.059423 4351.481 30 22 1.363636 1.625

8 50.5 21.5 29 0.067912 4506.891 30 23 1.304348 1.65625

9 51 21 30 0.076401 4662.301 31 23 1.347826 1.6875

10 52 20 32 0.08489 4973.121 36 24 1.5 1.875

9 50 21 29 0.076401 4506.891 31 23 1.347826 1.6875

8 49.5 21.5 28 0.067912 4351.481 30 22 1.363636 1.625

7 49 22 27 0.059423 4196.071 29 22 1.318182 1.59375

6 49 22 27 0.050934 4196.071 27 22 1.227273 1.53125

5 48.5 23 25.5 0.042445 3962.956 24 21 1.142857 1.40625

4 48 23.5 24.5 0.033956 3807.545 23 21 1.095238 1.375

3 48 23.5 24.5 0.025467 3807.545 22 21 1.047619 1.34375

2 47 24.5 22.5 0.016978 3496.725 19 19 1 1.1875

1 41 30 11 0.008489 1709.51 17.5 17.5 1 1.09375

0 36 36 0 0 0 16 16 1 1

58

At 137.4 rpm,Hs-16cm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 36 36 0 0 0 16 16 1 1

1 43 29 14 0.008489 2175.74 17 17 1 1.0625

2 47.5 24 23.5 0.016978 3652.135 19 19 1 1.1875

3 48 23.5 24.5 0.025467 3807.545 21 20 1.05 1.28125

4 48.5 23 25.5 0.033956 3962.956 23 21 1.095238 1.375

5 49 23 26 0.042445 4040.661 24 21 1.142857 1.40625

6 49.5 22 27.5 0.050934 4273.776 27 21.5 1.255814 1.515625

7 49.5 22 27.5 0.059423 4273.776 29 22 1.318182 1.59375

8 50.5 21 29.5 0.067912 4584.596 31 22 1.409091 1.65625

9 51 21 30 0.076401 4662.301 31 23 1.347826 1.6875

10 52 20 32 0.08489 4973.121 32 23.5 1.361702 1.734375

9 50 21 29 0.076401 4506.891 31 23 1.347826 1.6875

8 50 21.5 28.5 0.067912 4429.186 29 22.5 1.288889 1.609375

7 49.5 22 27.5 0.059423 4273.776 29 22 1.318182 1.59375

6 49 22 27 0.050934 4196.071 27 22 1.227273 1.53125

5 48 23 25 0.042445 3885.251 25 21 1.190476 1.4375

4 48 23 25 0.033956 3885.251 24 21 1.142857 1.40625

3 47 24 23 0.025467 3574.43 22 20 1.1 1.3125

2 46 25 21 0.016978 3263.61 20 19 1.052632 1.21875

1 42 29.5 12.5 0.008489 1942.625 17 17 1 1.0625

0 36 36 0 0 0 16 16 1 1

59

Material-Magnetite (dp-60µm)

At 73.9 rpm,Hs-16cm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 35 35.5 0 0 0 16 16 1 1

1 44.5 26.5 18.5 0.008489 2875.085 20 19 1.052632 1.21875

2 45 25 20.5 0.016978 3185.905 23 21 1.095238 1.375

3 45 25 20.5 0.025467 3185.905 24 21.5 1.116279 1.421875

4 45.5 24.5 21.5 0.033956 3341.315 25 22 1.136364 1.46875

5 46 24 22.5 0.042445 3496.725 27.5 22 1.25 1.546875

6 46 24 22.5 0.050934 3496.725 29 22.5 1.288889 1.609375

7 47 23 24.5 0.059423 3807.545 32 23 1.391304 1.71875

8 47 23 24.5 0.067912 3807.545 34 23 1.478261 1.78125

9 47 23 24.5 0.076401 3807.545 37 24 1.541667 1.90625

10 47.5 22.5 25.5 0.08489 3962.956 41 24 1.708333 2.03125

9 47 23 24.5 0.076401 3807.545 38 24 1.583333 1.9375

8 47 23 24.5 0.067912 3807.545 36 23 1.565217 1.84375

7 47 23 24.5 0.059423 3807.545 35 23 1.521739 1.8125

6 46.5 23.5 23.5 0.050934 3652.135 33 22.5 1.466667 1.734375

5 46 24 22.5 0.042445 3496.725 29 22 1.318182 1.59375

4 45 25 20.5 0.033956 3185.905 28 21 1.333333 1.53125

3 45 25 20.5 0.025467 3185.905 25 20 1.25 1.40625

2 45 25 20.5 0.016978 3185.905 23 18 1.277778 1.28125

1 44 26 18.5 0.008489 2875.085 20 19 1.052632 1.21875

0 35 35.5 0 0 0 16 16 1 1

60

At 101.6rpm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 35 35.5 0 0 0 16 16 1 1

1 45 26 19.5 0.008489 3030.495 20.5 19.5 1.051282 1.25

2 45 25 20.5 0.016978 3185.905 22 20 1.1 1.3125

3 46 24.5 22 0.025467 3419.02 24 20 1.2 1.375

4 46 24 22.5 0.033956 3496.725 26 20 1.3 1.4375

5 46 24 22.5 0.042445 3496.725 28 21 1.333333 1.53125

6 48 22 26.5 0.050934 4118.366 31 23 1.347826 1.6875

7 48 21.5 27 0.059423 4196.071 33 23 1.434783 1.75

8 48 21 27.5 0.067912 4273.776 36 23 1.565217 1.84375

9 48 21 27.5 0.076401 4273.776 39 24 1.625 1.96875

10 48 20.5 28 0.08489 4351.481 42 25 1.68 2.09375

9 48 21 27.5 0.076401 4273.776 40 24 1.666667 2

8 48 21.5 27 0.067912 4196.071 38 24 1.583333 1.9375

7 47 22 25.5 0.059423 3962.956 36 23 1.565217 1.84375

6 47 22 25.5 0.050934 3962.956 33 22 1.5 1.71875

5 47 22 25.5 0.042445 3962.956 31 21 1.47619 1.625

4 46 23 23.5 0.033956 3652.135 27 20 1.35 1.46875

3 45 24 21.5 0.025467 3341.315 24 19 1.263158 1.34375

2 44 25 19.5 0.016978 3030.495 22 19 1.157895 1.28125

1 43 26 17.5 0.008489 2719.675 21 19 1.105263 1.25

0 35 35.5 0 0 0 16 16 1 1

61

At 121.2 rpm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 35 35.5 0 0 0 16 16 1 1

1 44.5 25 20 0.008489 3108.2 21 20 1.05 1.28125

2 46 24 22.5 0.016978 3496.725 23 20 1.15 1.34375

3 46 24 22.5 0.025467 3496.725 26 20 1.3 1.4375

4 47 23 24.5 0.033956 3807.545 29 21 1.380952 1.5625

5 47 23 24.5 0.042445 3807.545 31 22 1.409091 1.65625

6 47 23 24.5 0.050934 3807.545 32 24 1.333333 1.75

7 47 23 24.5 0.059423 3807.545 33 24 1.375 1.78125

8 47.5 22 26 0.067912 4040.661 35 24 1.458333 1.84375

9 48 21 27.5 0.076401 4273.776 37 24 1.541667 1.90625

10 48 21 27.5 0.08489 4273.776 39 25 1.56 2

9 48 21 27.5 0.076401 4273.776 38 25 1.52 1.96875

8 47 22 25.5 0.067912 3962.956 36 24 1.5 1.875

7 47 22 25.5 0.059423 3962.956 34 24 1.416667 1.8125

6 47 22.5 25 0.050934 3885.251 33 23 1.434783 1.75

5 46 23 23.5 0.042445 3652.135 31 22 1.409091 1.65625

4 46 23 23.5 0.033956 3652.135 29 22 1.318182 1.59375

3 45 24 21.5 0.025467 3341.315 26 21 1.238095 1.46875

2 44 25 19.5 0.016978 3030.495 23 20 1.15 1.34375

1 44 25 19.5 0.008489 3030.495 21 19 1.105263 1.25

62

At 137.4 rpm

Flow

Rate(lpm


)

Hmin(cm

)

r R

0 35 35.5 0 0 0 16 16 1 1

1 43 24 19.5 0.008489 3030.495 21 20 1.05 1.28125

2 44 23 21.5 0.016978 3341.315 23 21 1.095238 1.375

3 44 23 21.5 0.025467 3341.315 25 22 1.136364 1.46875

4 44 23 21.5 0.033956 3341.315 26 23 1.130435 1.53125

5 45 22 23.5 0.042445 3652.135 28 223 0.125561 7.84375

6 45 22 23.5 0.050934 3652.135 30 24 1.25 1.6875

7 45 22 23.5 0.059423 3652.135 31 25 1.24 1.75

8 46 21 25.5 0.067912 3962.956 33 25 1.32 1.8125

9 46 21 25.5 0.076401 3962.956 35 26 1.346154 1.90625

10 46 21 25.5 0.08489 3962.956 37 26 1.423077 1.96875

9 46 21 25.5 0.076401 3962.956 36 26 1.384615 1.9375

8 45.5 22 24 0.067912 3729.84 34 25 1.36 1.84375

7 45 23 22.5 0.059423 3496.725 33 25 1.32 1.8125

6 45 23 22.5 0.050934 3496.725 31 24 1.291667 1.71875

5 44 24 20.5 0.042445 3185.905 30 24 1.25 1.6875

4 44 24 20.5 0.033956 3185.905 29 23 1.26087 1.625

3 43 25 18.5 0.025467 2875.085 27 22 1.227273 1.53125

2 43 25 18.5 0.016978 2875.085 24 21 1.142857 1.40625

1 43 25 18.5 0.008489 2875.085 22 21 1.047619 1.34375

0 35 35.5 0 0 0 16 16 1 1

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